Is 1464 a Prime Number?
2026-02-28 09:53 Diff
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Last updated on August 5, 2025

The numbers that have only two factors, which are 1 and itself, are called prime numbers. For encryption, computer algorithms, barcode generation, prime numbers are used. In this topic, we will be discussing whether 1464 is a prime number or not.

Is 1464 a Prime Number?

There are two types of numbers, mostly — Prime numbers and composite numbers, depending on the number of factors. A prime number is a natural number that is divisible only by 1 and itself. For example, 3 is a prime number because it is divisible by 1 and itself.

A composite number is a positive number that is divisible by more than two numbers. For example, 6 is divisible by 1, 2, 3, and 6, making it a composite number.

Prime numbers follow a few properties like:

  • Prime numbers are positive numbers always greater than 1.
  • 2 is the only even prime number.
  • They have only two factors: 1 and the number itself.
  • Any two distinct prime numbers are co-prime numbers because they have only one common factor, which is 1.
  • As 1464 has more than two factors, it is not a prime number.

Why is 1464 Not a Prime Number?

The characteristic of a prime number is that it has only two divisors: 1 and itself. Since 1464 has more than two factors, it is not a prime number. Several methods can be used to distinguish between prime and composite numbers. A few methods are:

  1. Counting Divisors Method
  2. Divisibility Test
  3. Prime Number Chart
  4. Prime Factorization

Using the Counting Divisors Method

The method in which we count the number of divisors to categorize the numbers as prime or composite is called the counting divisors method. Based on the count of the divisors, we categorize prime and composite numbers.

  • If there is a total count of only 2 divisors, then the number would be prime.
  • If the count is more than 2, then the number is composite.

Let’s check whether 1464 is prime or composite.

Step 1: All numbers are divisible by 1 and itself.

Step 2: Divide 1464 by 2. It is divisible by 2, so 2 is a factor of 1464.

Step 3: Divide 1464 by 3. It is not divisible by 3, so 3 is not a factor of 1464.

Step 4: You can simplify checking divisors up to 1464 by finding the root value. We then need to only check divisors up to the root value.

Step 5: When we divide 1464 by numbers like 2, 4, 6, and others, it is divisible by some of them.

Since 1464 has more than 2 divisors, it is a composite number.

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Using the Divisibility Test Method

We use a set of rules to check whether a number is divisible by another number completely or not. It is called the Divisibility Test Method.

Divisibility by 2: The number in the ones' place value is 4. Since 4 is an even number, 1464 is divisible by 2.

Divisibility by 3: The sum of the digits in the number 1464 is 15. Since 15 is divisible by 3, 1464 is also divisible by 3.

Divisibility by 5: The unit’s place digit is 4. Therefore, 1464 is not divisible by 5.

Divisibility by 7: The last digit in 1464 is 4. To check divisibility by 7, double the last digit (4 × 2 = 8). Then, subtract it from the rest of the number (146 - 8 = 138). Since 138 is divisible by 7, 1464 is also divisible by 7.

Divisibility by 11: In 1464, the alternating sum of the digits is 1 - 4 + 6 - 4 = -1. Since -1 is not divisible by 11, 1464 is not divisible by 11.

Since 1464 is divisible by numbers other than 1 and itself, it has more than two factors. Therefore, it is a composite number.

Using Prime Number Chart

The prime number chart is a tool created by using a method called “The Sieve of Eratosthenes.” In this method, we follow the following steps.

Step 1: Write 1 to 100 in 10 rows and 10 columns.

Step 2: Leave 1 without coloring or crossing, as it is neither prime nor composite.

Step 3: Mark 2 because it is a prime number and cross out all the multiples of 2.

Step 4: Mark 3 because it is a prime number and cross out all the multiples of 3.

Step 5: Repeat this process until you reach the table consisting of marked and crossed boxes, except 1. Through this process, we will have a list of prime numbers from 1 to 100.

Since 1464 is not in this range, we can conclude that it is not a prime number based on its divisibility by numbers within this range.

Using the Prime Factorization Method

Prime factorization is a process of breaking down a number into prime factors. Then multiply those factors to obtain the original number.

Step 1: We can write 1464 as 2 × 732.

Step 2: In 2 × 732, 732 is a composite number. Further, break the 732 into 2 × 366.

Step 3: Continue factorization: 2 × 183.

Step 4: Further factorize 183 into 3 × 61, where 61 is a prime number.

Step 5: Now we get the product consisting of only prime numbers.

Hence, the prime factorization of 1464 is 2 × 2 × 2 × 3 × 61.

Common Mistakes to Avoid When Determining if 1464 is Not a Prime Number

When learning about prime numbers, some common misconceptions can arise. Here are some mistakes that might be made.

FAQ on is 1464 a Prime Number?

1.What is 1464 divisible by?

1464 is divisible by 1, 2, 3, 4, 6, 8, 12, 24, 61, 122, 183, 244, 366, 488, 732, and 1464.

2.What is the sum of the divisors of 1464?

The sum of the divisors of 1464 is 3708.

3.What is the prime factorization of 1464?

The prime factorization of 1464 is 2 × 2 × 2 × 3 × 61.

4.What are the factors of 1464?

1464 is divisible by 1, 2, 3, 4, 6, 8, 12, 24, 61, 122, 183, 244, 366, 488, 732, and 1464, making these numbers the factors.

5.What are the closest prime numbers to 1464?

1459 and 1471 are the closest prime numbers to 1464.

Important Glossaries for "Is 1464 a Prime Number"

  • Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 1464 is a composite number because it is divisible by numbers like 1, 2, 3, 4, 6, 8, 12, 24, etc.
  • Prime factorization: The process of breaking down a number into its prime factors. For example, the prime factorization of 1464 is 2 × 2 × 2 × 3 × 61.
  • Divisibility rules: A set of rules that help us determine whether a number is divisible by another number. For example, a number is divisible by 3 if the sum of its digits is divisible by 3.
  • Prime number: A natural number greater than 1 that has no positive divisors other than 1 and itself. For example, 61 is a prime number.
  • Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.

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Hiralee Lalitkumar Makwana

About the Author

Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.

Fun Fact

: She loves to read number jokes and games.